A014325 Four-fold convolution of Bell numbers with themselves.

1, 4, 14, 48, 169, 624, 2442, 10188, 45452, 217100, 1109914, 6064584, 35330715, 218788432, 1435302930, 9940062428, 72422364227, 553338786504, 4420324121772, 36820875272488, 319053830821880, 2869645346679368, 26739383194844404, 257682847299543248

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..575

Formula

G.f.: (1/(1 - x - x^2/(1 - 2*x - 2*x^2/(1 - 3*x - 3*x^2/(1 - 4*x - 4*x^2/(1 - ...))))))^4, a continued fraction. - Ilya Gutkovskiy, Sep 25 2017

G.f.: ( Sum_{j>=0} A000110(j)*x^j )^4. - G. C. Greubel, Jan 08 2023

Mathematica

A014322[n_]:= Sum[BellB[j]*BellB[n-j], {j, 0, n}];
A014325[n_]:= Sum[A014322[j]*A014322[n-j], {j, 0, n}];
Table[A014325[n], {n, 0, 40}] (* G. C. Greubel, Jan 08 2023 *)

Prog

(Magma)
A014322:= func< n | (&+[Bell(j)*Bell(n-j): j in [0..n]]) >;
A014325:= func< n | (&+[A014322(j)*A014322(n-j): j in [0..n]]) >;
[A014325(n): n in [0..40]]; // G. C. Greubel, Jan 08 2023
(SageMath)
def A014322(n): return sum(bell_number(j)*bell_number(n-j) for j in range(n+1))
def A014325(n): return sum(A014322(j)*A014322(n-j) for j in range(n+1))
[A014325(n) for n in range(41)] # G. C. Greubel, Jan 08 2023

Crossrefs

Cf. A000110, A014322, A014323.

Column k=4 of A292870.

Sequence in context: A085280 A007851 A368555 * A047028 A220819 A047138

Adjacent sequences: A014322 A014323 A014324 * A014326 A014327 A014328

Keyword

nonn

Author

N. J. A. Sloane

Status

approved